The present invention relates to communications systems in general and, more specifically, to a method and apparatus for efficiently determining a channel estimate and a baud frequency offset estimate for a communications channel between a transmitter and a receiver.
FIGS. 1-2 respectively show models of a typical Quadrature Amplitude Modulation (QAM) transceiver 10 and a typical Carrierless Amplitude-Phase (CAP) transceiver 12 on a communications channel. Assuming perfect synchronization of the transmitter and receiver, a system may be modelled by the equation v=u*h+n (shown diagrammatically in FIG. 3), wherein v is the complex received signal, u is a transmitted complex symbol sequence, h is a complex channel model, and n is a complex noise signal. The complex noise signal is not assumed to be a white noise signal.
One goal of a characterization of a channel is to find a channel estimate, ĥ, that minimizes the expectation value (EV) of the difference between any given received signal and the expected signal. One formula for EV is shown as Equation 1.                     EV        =                  E          ⁢                      {                                          "LeftBracketingBar"                                  v                  -                                      u                    *                                          h                      ^                                                                      "RightBracketingBar"                            2                        }                                              (Equ.  1)            
Once known, channel estimate Ii can be used by a decoder for determining the appropriate decoder parameters, such as equalizer coefficients.
Further, in a real system, the clocks at the transmitter and receiver are not perfectly synchronized. The difference between the frequency of the transmitter""s clock and the receiver""s clock is called the baud frequency offset. Typically, the receiver would use some type of a timing recovery loop to track the differences in clock rates. To optimize performance in a packet-based demodulator, it""s valuable to also have an estimate of the baud frequency offset to initialize the timing recovery loop before starting demodulation of the packet.
Optimal sequences for obtaining channel estimates have long been understood. See, for example, J. Letaief and R. D. Murch""s, xe2x80x9cComplex Optimal Sequences with Constant Magnitude for Fast Channel Estimation Initializationxe2x80x9d, IEEE Trans. Comm., vol. 46, no3, p. 305-308, March 1998, and Simon Haykin""s xe2x80x9cAdaptive Filter Theory, 3rd Editionxe2x80x9d, Prentice-Hall, Inc. 1996, p 498. However, many methods for channel estimation require high computational complexity or a long preamble, or they don""t offer a convenient means of also obtaining an estimate of the baud frequency offset.
Therefore, a need exists for an efficient method and apparatus for determining both the channel estimate and the baud frequency offset estimate. The present invention provides such method and apparatus, wherein a type of preamble sequence and a computational structure obtains both a channel estimate and a baud frequency offset estimate using a minimal number of preamble symbols and having a very low computational complexity.
In accordance with the present invention, an efficient method and apparatus for obtaining a channel estimate and a baud frequency offset estimate for a communications channel in a communications system is provided. The communications system has a transmitter for transmitting to a receiver over the communications channel signals representing data appended to a preamble signal. The preamble signal is provided as a periodic plurality of preamble sequences, each preamble sequence being generated in accordance with:             1      32        ⁢                            ∑          15                          k          =          0                    ⁢                        b          k                ⁢                  b                      mod            ⁡                          (                                                k                  +                  n                                ,                16                            )                                *                      =      {                                                      1              ,                                                          n              =              0                                                                          0              ,                                                          n              ≠              0                                          .      
A transmission signal representing the periodic plurality of preamble sequences prepended to the data is sent by a transmitter over the communications channel to a receiver and is received at the receiver as a received signal. The received signal is processed to determine from the received signal both:
a) a channel estimate in accordance with:       h    ^    =            1      64        ⁢                  B        H            ⁢              (                              y            1                    +                      y            2                          )            
wherein B represents a matrix of preamble symbol values, upsampled by four and zero-filled, and y1 and y2 are column vectors of received samples; and
b) a baud frequency offset estimate xcex94fb in accordance with:       S    =                            ∑          63                          k          =          0                    ⁢                        y          k                ⁢                  y                      k            +            64                    *                                Δ      ⁢              xe2x80x83            ⁢              f        b              ≅                            real          ⁡                      (            S            )                          ·                  f          b                                                  imag            ⁡                          (              S              )                                ·                      f            c                    ·          32                ⁢                  xe2x80x83                ⁢        π            
wherein fb is the baud frequency and fc is the center frequency of the transmission signal.